Question

3 by 4 rectangle is inscribed in a circle. what's the circumfrence

Answer 1

The trick here is the recognize that the diagonal length of the rectangle is the diameter of the circle. 

W = width of rectangle = 4
L = length of rectangle = 3
D = diagonal of rectangle

Using pythagorean theorem, we solve for D.

W^2 + L^2 = D^2
(4)^2 + (3)^2 = D^2
16 + 9 = D^2
25 = D^2
5 = D or -5 = D

Since D is a length, D must be positive. Therefore, D=5.

D = diagonal of the rectangle = 5

Since D is also the diameter of the circle AND the diameter of a circle is twice the radius, we have the following equation :

r = radius of circle = 1/2 D = 1/2 (5) = 2.5
C = circumference

C = 2 pi r = 2 pi (2.5) = 5 pi